Mechanisms of chaos version

There are several mechanisms that act on the minor bodies of the solar system, making their orbits chaotic (click here to know what is a chaotic orbit) and giving birth to NEOs (dict.). These mechanisms can be separated into physical (such as collisions) and dynamical (such as the gravitational action of a nearby planet, or the phenomena of resonances).


A laboratory experiment on fragmentation (Courtesy of Ian Giblin, Ph.D Thesis, 1994 )

Collisions often happen between the very numerous asteroids that inhabit the main Belt (asteroid and Main belt, dict.), with a very complicated physic. Basically, two main phenomena can take place after a collision between asteroids: accretion and fragmentation.
The first case takes place when two bodies collide with a sufficiently small relative speed and stick together, forming a new, bigger body.
Fragmentation happens when the collision between the two bodies happens with a higher relative speed (or if the chemical composition of the two asteroids is more fragile). In this case the two bodies will give birth to smaller bodiesthat will either escape toward a new life, as single asteroids, either give birth to dynamical families of asteroids. Normally, the first hypothesis is not very usual and the collisions between the asteroids of the Main Belt are not enough energetic to make these objects become NEOs.
Fly-by of a planet

The orbit of any body of the solar system can be calculated, in a first, very approximated determination, considering the only gravitational attraction of the Sun. The main exception takes place when the body comes near a planet. In this case, when the body enters the zone where the attraction of the planet is fundamental (the sphere of influence of the planet) its original orbit is drastically changed to a new one, that can be determined considering only the gravitational attraction of the planet and neglecting any other gravitational force that acts on it. In a first approximation, this new orbit is independent from the original, old trajectory, but it is very sensible to the initial conditions of the actual motion (the conditions of the body just before it enters the sphere) : for this reason this mechanism can be seen as an amplificator of chaos.

A 2:1 resonant orbit

Resonance is an additional phenomenon which is very efficient in making the orbit change into a chaotic one and its parameters vary. The characteristic timescales are much longer than our lives (millions or hundred of millions of years) but, due to the high number of objects involved, these phenomena are fundamental in the transferring objects from stable to unstable orbits.
But what is resonance ?
Let's consider an asteroid with an orbit close to Jupiter.The Newton attraction force between two bodies is inversely proportional to their distance, so, when the two bodies come to their closest approach, the asteroid receives its maximum pull from the planet, which contributes to move it from its original orbit. If the periods of Jupiter and the asteroid are not proportional, the two bodies come close to each other randomly, and the overall effect of the attraction between them is null. On the other hand, the interaction between Jupiter and the asteroid is not negligible when the orbits of the two bodies have resonant periods, meaning that the period of the asteroid is a fraction of the period of Jupiter (for example, in the picture Jupiter has a period which is twice the asteroid's one). In these cases the perturbation is maximum, and the asteroid's orbit is unstable.
Yarkovski effect

Named for the Russian engineer who discovered it a century ago, the Yarkovsky effect results from the way a spinning asteroid absorbs and reradiates solar energy. Because an asteroid's surface gets hotter the longer sunlight falls on it, it does not reradiate energy evenly throughout its day or year. If different parts of the surface don't reemit radiation equally, the asteroid will receive a net kick in a particular direction, just as a rocket spewing a jet of gas recoils in the opposite direction. The smaller the asteroid, the greater the Yarkovsky effect. This could explain why the tiniest members of one family of asteroids, known as the Astrids, have the widest range of orbits, Farinella and Vokrouhlicky note.

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